Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C251 · Schur multiplier (H2) = C27×C4 |
| direct product | #3549×C251 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C251 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C251 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C251 ◁ G | |
1258 conjugacy classes of subgroups; only the 768 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 768 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8032 |
9538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 2281);